If the elliptical galaxy in Hydra, shown at the bottom of Figure 23-16 (Universe, 11th ed.), were to be at a distance of 3 billion ly, what would be a lower limit to the age of the universe? (Be careful with units.)
A)0.47 billion years
B)4.5 billion years
C)15 million years
D)15 billion years

Question

Quizplus · Accepted Answer

The age of the universe can be estimated using the Hubble law which states that the recessional velocity of a galaxy is proportional to its distance from us. By measuring the recessional velocity of a galaxy, we can determine its distance from us and thus estimate the age of the universe. The recessional velocity of the elliptical galaxy in Hydra is given as approximately 1600 km/s in the book. Converting this to distance using the Hubble constant of 70 km/s/Mpc, we get a distance of approximately 42 Mpc or 138 million ly. If this galaxy were to be at a distance of 3 billion ly (3000 million ly), then its recessional velocity would be much higher, indicating a much faster expansion of the universe in the past. Using the same Hubble constant and the distance of 3 billion ly, we can estimate the age of the universe as (3 billion ly)/(70 km/s/Mpc) = 42.8 billion years. However, it should be noted that this is a lower limit to the age of the universe as it assumes that the universe has been expanding at a constant rate, which is not true. The actual age of the universe is estimated to be around 13.8 billion years.

If the Elliptical Galaxy in Hydra, Shown at the Bottom